ANOTHER PROOF OF A SLOW CONVERGENCE RESULT OF BIRGE

被引：13

作者：

DEVROYE, L ^{[1
]}

机构：

[1] MCGILL UNIV,SCH COMP SCI,MONTREAL,PQ H3A 2A7,CANADA

来源：

STATISTICS & PROBABILITY LETTERS | 1995年 / 23卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

DENSITY ESTIMATION; NONPARAMETRIC ESTIMATION; LOWER BOUNDS; MINIMAX THEORY; RATE OF CONVERGENCE;

D O I：

10.1016/0167-7152(94)00095-P

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We give a short proof of the following result. Let f(n) be any density estimate based upon an i.i.d. sample drawn from a density f. For any monotone decreasing sequence {a(n)} of positive numbers converging to zero with a(1) less than or equal to 1/32, a density f may be found such that E{integral\f(n)(x)-f(x)\dx}greater than or equal to a(n) for all n. This density may be picked from the class of densities on [0,1] that are bounded by two. The proof of this fact simplifies an earlier proof by Birge (1986) and extends a weaker lower bound by the author (1983).

引用

页码：63 / 67

页数：5